A 1400 kg automobile is moving at a speed of 90 kmh when the

A 1400 kg automobile is moving at a speed of 90 km/h when the brakes are fully applied, causing the wheels to skid. Determine the time required to stop the automobile (a) on dry pavement (mu+k = 0.80), (b) on an icy road (mu_k = 0.10).

Solution

(a) maxinum frictional force between tyres and on dry pavement is

F=uR=uMg u-cofficient of friction

Retardation ,a=F/M=.80g

now we know v=u1+at

0=(90*5/18 ) -.80gt

.80gt=25

t=25/.80*9.8=3.18s

(b)

maxinum frictional force between tyres and on ice road is

F=uR=uMg u-cofficient of friction

Retardation ,a=F/M=.10g

as we know, v=u1+at

0=(90*5/18) -.10gt

.10gt = 25

t=25/.10*9.8=25.5 s